It has carved a place in counter-cultural history – a concrete enclave on London's South Bank beloved by skateboarders that has appeared in countless magazines and films.

The undercroft at the Southbank Centre is hailed as the birthplace of British skateboarding, a spot that has nurtured the homegrown talents of skateboard professionals such as Lewis "Chewie" Cannon, Ben Fairfax and Joey Pressey. The space is also used by BMX bikers and graffiti artists, and has become the urban arts foil to the high cultural offerings of the Southbank Centre.

"South Bank is a famous and legendary spot. People travel from all over the world to come here," said Pressey. It also features in Tony Hawk's Pro Skater 4 video game.

But the undercroft, which has also become a tourist draw, is under threat as part of plans to refurbish the ageing infrastructure of the Festival Wing, home to the Queen Elizabeth Hall, the Purcell Room and the Hayward Gallery.

"When I heard on the radio they were going to close this place down, I just couldn't wait around to see what would happen," said Duncan Pierce, a 24-year-old software engineering student from Colombo in Sri Lanka, who first came across the park two years ago. He and his girlfriend started an online petition and created a Facebook page for a campaign to save the South Bank skatepark. They have more than 4,000 signatures, but are aiming for 10,000. A three-day event of sport, arts and music will be held at the skatepark over the May bank holiday weekend to highlight their cause.

Pierce, though, may need to do more to derail the £120m plans to overhaul what the Southbank Centre's artistic director, Jude Kelly, has described as a "tired and undernourished" site.

"The undercroft site is absolutely fundamental and pivotal to the whole of the Festival Wing project," said Mike McCart, the Southbank Centre's director of partnership and policy. "It's pivotal both physically and financially – it will provide the only entrance into the heart of the cultural centre, and it's the most valuable financial part of the site."

The proposals for the Festival Wing would see the undercroft replaced by retail units, which are expected to pay for a third of the financing for the refurbishment.

"There are enough retail shops in London," said Chris Wass, who brought his 12-year-old son, Finlay, and his friend Moses from Brighton to skate at the undercroft. "This is somewhere where kids can hang out and they've got something to do. Taking that away, where are they going to go?"

McCart, however, is adamant that skateboarding will remain part of the South Bank. The centre has identified a space under the Hungerford bridge, the railway span that crosses the river from Charing Cross station. "We're making a commitment to make it a permanent space, a commitment to invest in it with them," he said. McCart recruited a research team at Central St Martins art and design college, with which the Southbank Centre had previously collaborated on a graffiti art event. The team at CSM began a consultation process with undercroft users at the end of February. The refurbishment plans were unveiled in the beginning of March.

"It's a sad fact that it's late in the stage," said CSM's Marcus Willcocks, who is co-ordinating the consultation process. "We had a week or less to organise and start talking to people before the plans were unveiled."

So far, through on-site visits to the undercroft and via a website, the consultation process has attracted only 118 names of people interested in having a say on what will happen to the skatepark.

Working groups are looking at different issues, such as alternative funding opportunities so that the existing skatepark can be retained. Another group is looking at the more probable scenario of how a new skate park under the Hungerford bridge would be designed.

Winstan Whitter, a film-maker who has documented the skateboarding culture at the South Bank through his films, is part of the process. He seems resigned to the change, despite his past efforts to keep skateboarding alive on the South Bank.

"I'm pleading with them to at least keep a part of it there, rather than put in an EAT like you see on every high street," he said. "The other site, Hungerford bridge, has no history. It will take a long time to make its own history."

The urban history of skateboarding

The concrete box buildings sitting on the south of the Thames were Britain's tonic to post-War malaise when food was still rationed and the NHS was in its infancy. The minimal, brutalist architecture with its modern materials, wide terraces, labyrinthine walkways and slab benches fell in and out of fashion and much of the space went unused.

But skateboarders in London discovered the undercroft in the 1970s. The hard edges and smooth surfaces, ramps and benches that the public found unwelcoming, provided the ideal environment for the new sport imported from the sunny shores of California. They've been a fixture at the site ever since.

"Skateboarders were the first real constituents of modernist urban design," writes the architect and skateboarding advocate Tony Bracali in his essay Thanks Le Corbusier (… from the Skateboarders) in reference to the French urbanist designer who heavily influenced post-war architecture and planning. "Skateboarding energised many of these poorly conceived and underutilised spaces with a new activity."

"Places where unexpected things happen were rarely designed for those unexpected things to happen," says Ricky Burdett, director of the London School of Economics Cities programme, which looks at how people interact with their urban environment. "The undercroft provides an audience. These activities are not about being secretive but about being part of a wider community. The fact that it's bang in your face with thousands of people moving up and down is exactly its appeal."